Weakly projective and weakly injective modules

Abstract

A module M is said to be weakly N-prvjective if it has a projective cover 7r: P (M)—» M and for each homomorphism (p: P (M)—> N there exists an epimorphism a: P (M)— >> M such that y (ker a)= 0, equivalently there exists a homomorphism (p: M—> N such that (pa= ip. A module M is said to be weakly projective if it is weakly/V-projective for all finitely generated modules N. Weakly AMnjective and weakly injective modules are defined dually. In this paper we study rings over which every weakly injective right/^-module is weakly ...